Steel and Composite Structures
Volume 28, Number 1, 2018, pages 13-24
DOI: 10.12989/scs.2018.28.1.013
Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter
Mohammed Sid Ahmed Houari, Aicha Bessaim, Fabrice Bernard, Abdelouahed Tounsi and S.R. Mahmoud
Abstract
A size-dependent novel hyperbolic shear deformation theory of simply supported functionally graded beams is presented in the frame work of the non-local strain gradient theory, in which the stress accounts for only the nonlocal strain gradients stress field. The thickness stretching effect (<i>ε<sub>z</sub></i> ≠ 0) is also considered here. Elastic coefficients and length scale parameter are assumed to vary in the thickness direction of functionally graded beams according to power-law form. The governing equations are derived using the Hamilton principle. The closed-form solutions for exact critical buckling loads of nonlocal strain gradient functionally graded beams are obtained using Navier's method. The derived results are compared with those of strain gradient theory.
Key Words
new hyperbolic shear theory; nonlocal strain gradient elasticity; stretching effect; buckling analysis
Address
(1) Mohammed Sid Ahmed Houari, Aicha Bessaim, Abdelouahed Tounsi:
Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de génie civil, Algeria;
(2) Mohammed Sid Ahmed Houari, Aicha Bessaim:
Département de génie civil, Faculté des Sciences et de la Technologie, Université de Mascara, Route de Mamounia 29000 Mascara, Algérie;
(3) Mohammed Sid Ahmed Houari, Aicha Bessaim, Abdelouahed Tounsi:
Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria;
(4) Fabrice Bernard:
Université Européenne de Bretagne, INSA Rennes, LGCGM, 20 avenue des Buttes de coësmes 35708 Rennes Cedex 7, France;
(5) Abdelouahed Tounsi:
Civil and Environmental Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia;
(6) Abdelouahed Tounsi:
Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria;
(7) S.R. Mahmoud:
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.